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Convergence of hitting times for jump-diffusion processes
Volume 2, Issue 3 (2015): PRESTO-2015, pp. 203–218
Georgiy Shevchenko ORCID icon link to view author Georgiy Shevchenko details  

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https://doi.org/10.15559/15-VMSTA32
Pub. online: 23 September 2015      Type: Research Article      Open accessOpen Access

Received
16 February 2015
Revised
7 September 2015
Accepted
7 September 2015
Published
23 September 2015

Abstract

We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the equations and of the moments when the solutions hit certain sets.

References

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Cont, R., Tankov, P.: Financial Modelling with Jump Processes. Chapman and Hall/CRC, Boca Raton (2004). MR2042661
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Mishura, Y.S., Tomashyk, V.V.: Convergence of exit times for diffusion processes. Theory Probab. Math. Stat. 88, 139–149 (2014)
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Moroz, A.G., Tomashyk, V.V.: Convergence of solutions and their exit times in diffusion models with jumps. Cybern. Syst. Anal. 50(2), 288–296 (2014). MR3276037. doi:10.1007/s10559-014-9616-6
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Pham, H.: Optimal stopping, free boundary, and American option in a jump-diffusion model. Appl. Math. Optim. 35(2), 145–164 (1997). MR1424787. doi:10.1007/s002459900042
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Situ, R.: Theory of Stochastic Differential Equations with Jumps and Applications. Springer, New York (2005). MR2160585
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Tomashyk, V.V., Shevchenko, G.M.: Convergence of hitting times in diffusion models with jumps and non-Lipschitz diffusion. Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2014(2), 32—38 (2014)
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Zhang, X.L.: Valuation of American options in a jump-diffusion model. In: Numerical Methods in Finance. Publ. Newton Inst., pp. 93–114. Cambridge Univ. Press, Cambridge (1997). MR1470511

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Keywords
Stochastic differential equation Poisson measure jump-diffusion process stopping time convergence

MSC2010
60H10 60G44 60G40

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